Basic Design Concepts
© 2006,2008 T. Bartlett Quimby
Limit State Concepts
Last Revised: 08/02/2008
In structural design, design constraints are frequently referred to as LIMIT STATES. Limit States are conditions of potential failure. Failure being defined as any state that makes the design to be infeasible (i.e. it will not work for its intended purpose).
Limit states take the general form of:
Demand < Capacity
Structural limit states tend to fall into two major categories: strength and serviceability.
Strength Limit States
Strength based limit states are potential modes of structural failure. For steel members, the failure may be either yielding (permanent deformation) or rupture (actual fracture). The strength based limit state can be written in the general form:
Required Strength < Nominal Strength
The required strength is the internal force that you derive from your analysis of the structure being designed. For example, when designing a beam, the required strength may be the maximum moment, M, computed for the beam. The nominal strength is the predicted capacity of the beam, for example in bending, it is the maximum moment, Mn, that the beam is capable of supporting (a function of the stress capacity of the material and the section properties of the member)
Typically the structural design specifications use the following variables to denote the different strengths:
P = Axial Force
Serviceability Limit States
Serviceability limit states are those conditions that are not strength based but still may make the structure unsuitable for its intended use. The most common serviceability limit states in structural design are deflection, vibration, slenderness, and clearance. Serviceability limit states can be written in the general form:
Actual Behavior < Allowable Behavior
An example of this is deflection. A loaded cantilever beam will have a deflection at the free end (actual behavior) that must be kept less that an allowable deflection (allowable behavior).
Serviceability limit states tend to be less rigid requirements than strength based limit states since the safety of the structure is not in question. Serviceability limit states don't tend to put people's lives at risk nor do they risk property damage.
Note that there uncertainties and variability associated with both sides of the limit state inequalities. How these uncertainties and variabilities are handled depends on which design philosophy you chose to use. There are two major design philosophies present in the current structural engineering practice: Load & Resistance Factor Design (LRFD) and Allowable Strength (or Stress) Design (ASD). These to philosophies are discussed in a following section.
It is worth noting that some engineers find it useful to divide the left side of the limit state inequalities by the right in the form:
(Required Strength/Nominal Strength) < 1.00
(Actual Behavior)/(Allowable Behavior) < 1.00
This form is useful for two reasons. It makes comparison easier (the resulting value must be < 1.00) and the resulting number tells you the percent of capacity used. Knowing the percent of capacity used will help you decide which limit states are critical as you work on optimizing a complex design problem.